President Mahmoud Abbas and Hamas political leader Khalid Mashaal will meet in Qatar Sunday to discuss a truce in Gaza, on day 13 of an Israeli offensive, an official said.

The official close to Abbas, speaking on condition of anonymity, said: "The president will meet Mashaal to discuss ways of reaching a ceasefire in the Gaza Strip," where Israel's campaign has killed more than 340 Palestinians since July 8.

Sunday's meeting comes after the Islamist movement that controls the coastal territory said it had passed on its conditions for a ceasefire to Abbas, Qatar, Turkey and the Arab League.

Hamas' conditions include "an end to aggression against the Palestinian people," lifting the blockade on the territory, and opening the Rafah border crossing with Egypt.

They also include freedom of movement for Gaza Palestinians in the area bordering Israel, freeing prisoners rearrested after being exchanged for a seized Israeli soldier, and extending the territory's fishing zone.

Injured man gives peace sign (image by Mohammad al-Qattawi @m_alqattawi on Twitter)The Israeli ground invasion continued for a second day straight on Saturday, claiming over 100 lives in the past two days, many of them children and families killed in their homes. This follows the killing of over 200 Palestinians in the previous nine days by massive airstrikes that targeted every part of the crowded coastal Strip. The latest escalation by Israeli forces follows an offer by the Hamas party in Gaza to negotiate a ten-year truce with Israel, which included the condition that the eight-year long siege on Gaza which has devastated the economy and livelihood of its 1.8 million inhabitants be lifted.

Israel rejected that offer, and instead launched a massive ground offensive into Gaza, which Israeli officials claim is meant to “root out the terrorists”, but which eyewitnesses on the ground say is mainly killing women and children, and pushing more Palestinians toward armed resistance.

On Saturday afternoon, 24 Palestinians were killed by Israeli airstrikes, tank shells and naval artillery shells. This brings the death toll on Saturday alone to 45 Palestinians, including 4 members of the Salhiyya family (3 adults and one child), 3 members of the Nassr family (2 adults and 1 child), and a 6-year old child killed in Khan Younis, all in the early morning hours of Saturday.

A 33-year old Palestinian citizen of Israel was killed by a Palestinian shell on Friday afternoon, and two young children and a woman wounded. The four members of the same family were hit by the shell in their home, in the unrecognized Bedouin village of Qasr al-Sir. Israeli authorities have not constructed bomb shelters in the Palestinian Bedouin villages, which have been ‘unrecognized’ by the state of Israel since Israel’s creation on Palestinian land in 1948. The residents of these villages have faced repeated demolitions of their homes and villages by Israeli authorities.

The Palestinians killed on Saturday afternoon include an entire family, including a 2 year old baby and 6-year old child, killed in their home.

The United Nations Refugee Works Administration, which runs many of the schools in Gaza, is currently struggling to provide assistance for the nearly 50,000 Palestinians that have fled from their homes in the north of the country into 44 UN schools.

Hamas' armed wing said Saturday that a group of its operatives infiltrated Israeli territory for the second time in a day and killed five Israeli soldiers.

The al-Qassam Brigades said the fighters tunneled under the Gaza border into Israeli territory near the Sufa crossing east of Rafah. Then they shot five soldiers dead, the group said.

It said three were killed by direct gunshots to the head, while the others suffered bullet wounds in other areas of their bodies.

Only hours earlier, the Israeli army announced the deaths of two soldiers by militants who had breached the Gaza border.

An army statement said those two, Sergeant Adar Bersano, 20, from Neharyia, and Major Amotz Greenberg, 45, from Hod Hasharon, were killed during a clash with a number of militants who infiltrated Israel through a tunnel from Gaza.

The fighters, also affiliated with Hamas' military wing, infiltrated the southern Israeli region of Eshkol near Ein HaShlosha through a tunnel and attacked an Israeli army patrol.

The Al-Qassam Brigades claimed responsibility for the raid in a statement, adding that "Heavy fighting is ongoing with the forces of the occupation."

The Israeli military said in a statement that militants opened fire on the attackers with machine guns and an anti-tank missile.

The military said that they returned fire and killed one of the militants, while the rest re-entered the tunnel and returned to Gaza.

It added that they pursued the attackers into Gaza.

The group had reported earlier on Saturday morning that it had breached "enemy lines" in the northern Gaza Strip and had engaged Israeli forces.

They said that they had managed to infiltrate Israeli lines in the area, which has witnessed heavy fighting since the beginning of the Israeli ground invasion late Thursday.

The Israeli army announced Saturday the deaths of two Israeli soldiers by militants who had breached the Gaza border, hours after they had been reported wounded.

An army statement said the two, Sergeant Adar Bersano, 20, from Neharyia, and Major Amotz Greenberg, 45, from Hod Hasharon, were killed during a clash with a number of militants who infiltrated Israel through a tunnel from Gaza.

The fighters, affiliated with Hamas' military wing, infiltrated the southern Israeli region of Eshkol near Ein HaShlosha through a tunnel and attacked an Israeli army patrol.

Hamas's military wing, the Al-Qassam Brigades, claimed responsibility for the raid in a statement, adding that "Heavy fighting is ongoing with the forces of the occupation."

The Israeli military said in a statement that militants opened fire on the attackers with machine guns and an anti-tank missile.

The military said that they returned fire and killed one of the militants, while the rest re-entered the tunnel and returned to Gaza.

It added that they pursued the attackers into Gaza.

The al-Qassam Brigades said earlier on Saturday morning that it had breached "enemy lines" in the northern Gaza Strip and had engaged Israeli forces.

They said that they had managed to infiltrate Israeli lines in the area, which has witnessed heavy fighting since the beginning of the Israeli ground invasion late Thursday.

The Ministry of Health of Gaza warned on Saturday of a “real disaster” due to power shortages, lack of power needed to operate machinery and a lack of necessary medical supplies and medicine.

The ministry's general director of medical stores said during a news conference on Saturday that hospitals lack medicines needed for emergencies and operations.

Ashraf Abu Mahadi added that “there will be a major crisis if medications are not available, especially anesthetics and intensive care. Basic medical supplies are all out and what we have in our warehouses will not be enough for days.”

Abu Mahadi said that “what has been used during the Israeli offensive is multiple times more than what we have received in the last couple of days.”

The general director of the ministry’s maintenance department warned of the repeated power shortages and lack of necessary power to operate machines. he said that hospitals have been using generators for the last couple of days because of the power shortages.

“Al-Shifaa Hospital uses one generator to operate. The al-Nasser medical center still works on generators, and power shortages damage the generators because they cannot keep operating round the clock,” Islam al-Hamadin added.

The European Hospital has been facing a blackout for 48 hours, he added.